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The symmetric periodic orbits for the two-electron atom

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Abstract

We analyse the existence of symmetric periodic orbits of the two-electron atom. The results obtained show that there exist six families of periodic orbits that can be prolonged from a continuum of periodic symmetric orbits. The main technique applied in this study is the continuation method of Poincaré.

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Acknowledgements

The first author is partially supported by the MINECO-FEDER Grant MTM2016-77278-P, a MINECO Grant MTM2013-40998-P and an AGAUR Grant Number 2014SGR-568. The second author is supported by PROCAD/CAPES Grant 88881.0 68462/2014-01 and by CNPq-Brazil.

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Authors and Affiliations

  1. Institute of Mathematics and Statistics, Federal University of Goiás, Avenida Esperança s/n, Campus Samambaia, Goiânia, Goiás, CEP 74690-900, Brazil

    Durval José Tonon

  2. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra, Barcelona, Spain

    Jaume Llibre

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  1. Jaume Llibre
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  2. Durval José Tonon
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Correspondence to Durval José Tonon.

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Llibre, J., Tonon, D.J. The symmetric periodic orbits for the two-electron atom. Lett Math Phys 108, 1851–1871 (2018). https://doi.org/10.1007/s11005-018-1056-1

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  • DOI: https://doi.org/10.1007/s11005-018-1056-1

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